Nonlinear coprime factorizations and parameterization of a class of stabilizing controllers

New definitions for the right, left and doubly-coprime factorizations for nonlinear, input-affine systems based on the notion of the state-to-output stability are introduced. Sufficient conditions for the existence of these factorizations as well as local state-space formulas of factors are given. Finally, these results are applied for obtaining a parameterized set of stabilizing controllers for a fairly broad class of plants, transforming the original feedback control configuration into the open loop model matching configuration and extending thus the classical Youla-Kucera parameterization to nonlinear local cases.